Effects of vorticity on the travelling waves of some shallow water two-component systems
Résumé
In the present study we consider three two-component (integrable and non-integrable) systems which describe the propagation of shallow water waves on a constant shear current. Namely, we consider the two-component Camassa-Holm equations, the Zakharov-Ito system and the Kaup--Boussinesq equations all including constant vorticity effects. We analyze both solitary and periodic-type travelling waves using the simple and geometrically intuitive phase space analysis. We get the pulse-type solitary wave solutions and the front solitary wave solutions. For the Zakharov-Ito system we underline the occurrence of the pulse and anti-pulse solutions. The front wave solutions decay algebraically in the far field. For the Kaup-Boussinesq system, interesting analytical multi-pulsed travelling wave solutions are found.
Domaines
Mécanique des fluides [physics.class-ph] Dynamique des Fluides [physics.flu-dyn] Analyse classique [math.CA] Physique mathématique [math-ph] Physique Atmosphérique et Océanique [physics.ao-ph] Systèmes Solubles et Intégrables [nlin.SI] Formation de Structures et Solitons [nlin.PS] Equations aux dérivées partielles [math.AP] Systèmes dynamiques [math.DS] Physique mathématique [math-ph] Géométrie algébrique [math.AG]Origine | Fichiers produits par l'(les) auteur(s) |
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